TY - BOOK ID - 211511 TI - Idempotent Matrices over Complex Group Algebras PY - 2006 SN - 3540279911 3540279903 PB - Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, DB - UniCat KW - Idempotents. KW - Matrices. KW - Group algebras. KW - Algebras, Group KW - Abelian groups KW - Locally compact groups KW - Algebra, Matrix KW - Cracovians (Mathematics) KW - Matrix algebra KW - Matrixes (Algebra) KW - Algebra, Abstract KW - Algebra, Universal KW - Idempotent elements KW - Algebras, Linear KW - Mathematical physics KW - Algebra. KW - K-theory. KW - Group theory. KW - Functional analysis. KW - Associative Rings and Algebras. KW - Category Theory, Homological Algebra. KW - K-Theory. KW - Group Theory and Generalizations. KW - Functional Analysis. KW - Functional calculus KW - Calculus of variations KW - Functional equations KW - Integral equations KW - Groups, Theory of KW - Substitutions (Mathematics) KW - Algebra KW - Algebraic topology KW - Homology theory KW - Mathematics KW - Mathematical analysis KW - Associative rings. KW - Rings (Algebra). KW - Category theory (Mathematics). KW - Homological algebra. KW - Homological algebra KW - Category theory (Mathematics) KW - Algebra, Homological KW - Group theory KW - Logic, Symbolic and mathematical KW - Topology KW - Functor theory KW - Algebraic rings KW - Ring theory KW - Algebraic fields KW - Rings (Algebra) UR - https://www.unicat.be/uniCat?func=search&query=sysid:211511 AB - The study of idempotent elements in group algebras (or, more generally, the study of classes in the K-theory of such algebras) originates from geometric and analytic considerations. For example, C.T.C. Wall [72] has shown that the problem of deciding whether a ?nitely dominated space with fundamental group? is homotopy equivalent to a ?nite CW-complex leads naturally to the study of a certain class in the reduced K-theoryK (Z?) of the group ringZ?. 0 As another example, consider a discrete groupG which acts freely, properly discontinuously, cocompactly and isometrically on a Riemannian manifold. Then, following A. Connes and H. Moscovici [16], the index of an invariant 0th-order elliptic pseudo-di?erential operator is de?ned as an element in the ? ? K -group of the reduced groupC -algebraCG. 0 r Theidempotentconjecture(alsoknownasthegeneralizedKadisonconjec- ? ? ture) asserts that the reduced groupC -algebraCG of a discrete torsion-free r groupG has no idempotents =0,1; this claim is known to be a consequence of a far-reaching conjecture of P. Baum and A. Connes [6]. Alternatively, one mayapproachtheidempotentconjectureasanassertionabouttheconnect- ness of a non-commutative space;ifG is a discrete torsion-free abelian group ? thenCG is the algebra of continuous complex-valued functions on the dual r ER -